Three-dimensional logical puzzles

ABSTRACT

Semiregular or irregular polyhedron-based puzzles have at least two different types of faces. The dividing method used to create the puzzles requires that bisecting planes parallel to the faces be chosen to exclude at least one type of face. Preferably, the base polyhedron has a Buckyball (soccer ball) shape. Applying this dividing method to a Buckyball polyhedron results in (i) a center element with six axes passing through geometrical centers of pentagonal faces, (ii) twelve pentagonal rotating elements, and (iii) thirty mobile elements of tetrahedral shape. The mobile elements are exchangeable between adjacent groups. In another embodiment, sliding elements are superimposed over the mobile elements to enable sliding motion in addition to shifting/rotating motion. Different indicia patterns can be used to modulate the difficulty level of the puzzle. The same dividing method can be used on a sphere to obtain a completely spherical puzzle.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority under 35 U.S.C. 119(e) from U.S.Provisional Patent Application Ser. No. 60/896,511 filed on Mar. 23,2007.

TECHNICAL FIELD

The present invention relates generally to three-dimensional logicalpuzzles and, in particular, to puzzles having either a spherical shapeor a shape based on a semiregular or irregular polyhedron.

BACKGROUND OF THE INVENTION

Since the introduction of the Rubik's Cube, numerous types ofshifting-movement polyhedron-shaped three-dimensional puzzles have beendisclosed. These various puzzles can be classified as regular,semiregular or irregular polyhedron-shaped puzzles, a classificationbased on Leonhard Euler's findings that all polyhedron patterns can bebroken down into three elements: (i) two-dimensional faces; (ii)one-dimensional edges; and (iii) zero-dimensional vertices.

For a polyhedron to be regular, the faces of the polyhedron must beidentical and the same number of faces must meet at each vertex (calledthe “valence”). Polyhedrons with only one kind of vertex (congruentvertex) but two different kinds of faces are called semiregular. Theremaining polyhedrons are classified as irregular. However, evenirregular polyhedreons follow Euler's law that the number of verticesplus the number of faces in every polyhedron must equal the number ofedges plus two.

The regular polyhedron family is surprisingly limited to only five, thetetrahedron (four triangular faces, six edges, and four tri-valentvertices), the cube (six cubic faces, twelve edges, and eight tri-valentvertices), the octahedron (eight triangular faces, twelve edges, and sixquadri-valent vertices), the dodecahedron (twelve pentagonal faces,thirty edges, twenty tri-valent vertices), and the icosahedron (twentytriangular faces, thirty edges, and twelve quintus-valent vertices).

The prior art of shifting-movement puzzles includes regular, semiregularand irregular polyhedrons. Aside from ubiquitous cubic puzzles, such asthe Rubik's Cube, there are numerous other types of polyhedron-basedpuzzles known in the art such as, for example, those based on a regulartetrahedron (e.g. U.S. Pat. No. 4,558,866 to Alford), a regularoctahedron (e.g. U.S. Pat. No. 4,451,039 to Hewlett, U.S. Pat. No.4,478,418 to Sherman, U.S. Pat. No. 4,496,155 to Goldfarb, U.S. Pat. No.4,557,484 to Sherman-Francis, U.S. Pat. Nos. 4,593,907 and 4,706,956 toAbu-Shumays and U.S. Pat. No. 4,593,908 to Ibrahim).

Furthermore, puzzles based on a regular dodecahedron are also known inthe art (e.g. U.S. Pat. No. 4,416,453 to Sasso, U.S. Pat. No. 4,506,891to Alexander-Piaget, U.S. Pat. No. 4,558,866 to Alford, U.S. Pat. No.4,600,199 to Krell, and U.S. Pat. No. 4,674,750 to Abu-Shumays).

Puzzles based on a regular icosahedron are described in U.S. Pat. No.4,473,228 to Hart, U.S. Pat. No. 4,474,376 to Gustafson, U.S. Pat. No.4,529,201 to Nadel, U.S. Pat. No. 4,575,088 to Peek, and U.S. Pat. No.4,706,956 to Abu-Shumays.

Semiregular cuboctahedron and icosidodecahedron puzzles are described inU.S. Pat. No. 4,478,418 to Sherman and in U.S. Pat. No. 4,557,484 toSherman-Francis.

Irregular rhombicosidodecahedron and irregular rhombic dodecahedronpuzzles are described, respectively, in U.S. Pat. No. 4,529,201 to Nadeland U.S. Pat. Nos. 4,593,907 and 4,674,750 to Abu-Shumays. Furthermore,puzzles based on an irregular prism, cross, diamond, and truncated cubeare described by Abu-Shumays in U.S. Pat. No. 4,593,907.

Furthermore, there exist a number of other irregular-polyhedron-typepuzzles based on an irregular heptahedron (e.g. U.S. Pat. No. 4,836,549to Flake), an irregular (so-called) hexagram (e.g. U.S. Pat. No.5,199,711 to Pataki et al.), an irregular mix of octahedron andtetrahedron (e.g. U.S. Pat. No. 5,386,993 to Apsan), an irregularstellated icosahedron (e.g. U.S. Pat. No. 4,529,201 to Nadel), as wellas other irregular polyhedrons (e.g. U.S. Pat. No. 4,500,090 to Nieto,U.S. Pat. No. 4,522,402 to Henry, U.S. Pat. No. 4,593,908 to Ibrahim,U.S. Pat. No. 4,600,199 to Krell, U.S. Pat. No. 5,722,657 to Cabrera,and U.S. Pat. No. 6,644,665 to Brooks.)

Also of interest in the prior art is U.S. Pat. No. 4,453,715 to Halpernwhich teaches an oblique twistable three-dimensional puzzle that uses,for example, a dodecahedron as the guiding polyhedron.

Also known in the art are three-dimensional sliding puzzles, such as thequasi Buckyball shaped sliding puzzle disclosed by Blazek and al. inU.S. Pat. No. 6,994,343.

Cubic puzzles having a combination of both sliding and shifting elementsis described by Kuchimanchi in U.S. Pat. No. 4,872,682 and Pop in U.S.Pat. No. 5,116,502.

Also known in the art are ball-shaped or spherical puzzles such as theone disclosed in U.S. Pat. No. 7,108,263 to Cabeza et al. The Cabezapuzzle is a sphere dissected by three vertical planes and threehorizontal planes. These orthogonal dissections of the sphere create twoorthogonal pairs of hemispheres which are further subdivided to createsix outer spherical sections. The hemispheres and outer sphericalsections (and the layers defined therebetween) can be rotated in twoorthogonal directions to enable both shifting and sliding movements.

Also known in the art are three-dimensional labyrinth puzzles, such asthe one taught by Fang et al. in U.S. Pat. No. 7,165,768. In the Fangpuzzle, a sphere is divided by two vertical planes and two horizontalplanes to enable rotation of the resulting elements. The elements havebores formed therein, defining tunnels to enable a small ball to travelwithin the tunnels from an entrance to an exit.

Despite the plethora of polydredon-based puzzles and spherical puzzlesthat are now known in the art, to the best of Applicant's knowledge,none of the semiregular or irregular polyhedron-based puzzles known inthe art enable both rotating/shifting movement in combination withsliding movement about one specific type of face. Therefore, asemiregular or irregular polyhedron-based puzzle enabling shifting (andoptionally also sliding movement) would provide a highly challenging,entertaining and aesthetically-pleasing three-dimensional puzzle.

As regards spherical puzzles, to the best of Applicant's knowledge, noneof the spherical puzzles known in the art are created by dividing asphere based on a guiding polyhedron, i.e. by defining outer sphericalsections by dividing the sphere parallel to a guiding polyhedron tocreate overlapping spherical sections on the sphere. A spherical puzzlecreated by this technique would be challenging, entertaining andaesthetically-pleasing.

SUMMARY OF THE INVENTION

An object of the present invention is to provide a challenging,entertaining and aesthetically pleasing semiregular or irregularpolyhedron-based puzzle having elements that can be shifted (i.e.twisted or rotated) to enable a user of the puzzle to rearrange themovable elements of the puzzle to attempt to restore color patterns, orthe like, displayed upon outer faces of the movable elements.

The present invention thus provides a three-dimensional puzzle havingeither a semiregular polyhedron shape or an irregular polyhedron shape,defining at least two different types of faces (or “pieces” or“elements”). For example, in a semiregular polyhedron, there would betwo different types of faces, a first set of faces and a second set offaces. The first set of faces is rotationally connected to a core orcenter element to define a plurality of rotating elements while thesecond set of faces are mobile elements grouped around each rotatingelement, as will be elaborated below.

In accordance with another aspect of the invention, the semiregular orirregular polyhedron-shaped puzzle can further include superimposedsliding elements that slide in grooves in the underlying faces so as toprovide a combination of sliding and shifting (“twisting” or rotational)movements, as a further challenge.

Another object of the present invention is to provide a challenging,entertaining and aesthetically-pleasing spherical puzzle.

Accordingly, another aspect of the present invention is a sphericalpuzzle having a sphere dissected into twelve overlapping outer sphericalsections that are created by “slicing” (i.e. sectioning or dividing) thesphere using cutting planes that are parallel to each one of the twelvepentagonal faces of a dodecahedron. In general, this spherical puzzleincludes an optional central core, such as a dodecahedron, a pluralityof rotating elements rotationally connected to the optional centralcore, each rotating element having a convex outer face defining aportion of a sphere, a plurality of first mobile elements connected toeach of the rotating elements, a plurality of second mobile elementsconnected to each of the rotating elements between each of the firstmobile elements, whereby the rotating elements, the first mobileelements and the second mobile elements together constitute a completesphere and wherein the rotating elements and their respective groups offirst and second mobile elements together define overlapping circles onthe sphere to enable interchanging of first and second mobile elementsof one group with first and second mobile elements of another adjacentgroup.

In accordance with yet another aspect of the invention, the sphericalpuzzle can further include superimposed sliding elements for sliding ingrooves formed in the underlying rotating and mobile elements to thusenable sliding movement in addition to shifting movement. The convexlyshaped superimposed sliding elements are clustered in non-overlappingcircles on the sphere to enable exchanging of sliding elements when theclusters are rotated.

Another object of the present invention is to provide athree-dimensional Buckyball or spherical puzzle that serves as anadvertising medium, particularly in the realm of sports where thepuzzles can be made to resemble or mimic sports balls. The outersurfaces of these puzzles can be used to display logos such as, forexample, corporate logos of sponsors or sports team logos.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments of the present invention will now be described withreference to the appended drawings in which:

FIG. 1 is an isometric view of a semiregular Buckyball-shaped polyhedronpuzzle in accordance with a first preferred embodiment, showing onegroup partially rotated;

FIG. 2 illustrates the six axes of the center element oriented as aregular dodecahedron polyhedron;

FIG. 3 is an isometric detailed view of a rotating element shaped likean angularly extruded pentagon;

FIG. 4 is a cross-sectional view of the rotating element taken alongline b-b of FIG. 3;

FIG. 5 is an isometric view of an opposed quasi-tetrahedron-shapedmobile element;

FIG. 6 shows an isometric view of the puzzle in accordance with a firstpreferred embodiment in which every rotating element is assembled on thecenter element, and also showing a cross section of one groupconstituted by one rotating element and a plurality of mobile elements;

FIG. 7 illustrates the dividing method used to cut out the rotating andmobile elements;

FIG. 8 illustrates the method used for interfitting rotating and mobileelements;

FIG. 9 is an isometric partial cross-sectional view of a rotatingelement in accordance with a second preferred embodiment thatincorporates a retaining groove;

FIG. 10 is an isometric view of a concealed mobile element in accordancewith the second preferred embodiment;

FIG. 11 shows a sliding element mainly shaped as an angularly extrudedequilateral triangle with a guiding tongue used in the second preferredembodiment;

FIG. 12 illustrates a view of the second preferred embodiment with anexploded view of a hexagonal cluster constituted of sliding elements;

FIG. 13 is an isometric view of the second preferred embodiment with anaugmented group containing five half-clusters rotated;

FIG. 14 shows possible physical locations of indicia patterns for thesecond preferred embodiment used to modulate the difficulty level of thepuzzle;

FIG. 15 illustrates an example of indicia patterns for the secondpreferred embodiment of a novice-level puzzle;

FIG. 16 illustrates an example of indicia patterns for the secondpreferred embodiment of an intermediate-level puzzle;

FIG. 17 illustrates an example of indicia patterns for the secondpreferred embodiment of an expert-level puzzle.

FIG. 18 is an isometric view of a spherical rotating element of thethird preferred embodiment shaped like a convex pentagon;

FIG. 19 is an isometric view of a spherical mobile element of the thirdpreferred embodiment;

FIG. 20 shows an isometric view of a spherical gap element of the thirdpreferred embodiment;

FIG. 21 shows an isometric view of the third preferred embodiment withan exploded view of a spherical group containing one spherical rotatingelement, five spherical mobile elements and five spherical gap elements;

FIG. 22 shows an isometric view of the fourth preferred embodimentillustrating an augmented spherical group and an augmented sphericalcluster;

FIG. 23 is an isometric view of a split hollow polyhedron center elementassembled from a snapping action of two half center core elementspartially shown; and

FIG. 24 shows a half center core element and another connecting meansfor mounting any of the rotating elements of the four preferredembodiments.

These drawings are not necessarily to scale, and therefore componentproportions should not be inferred therefrom.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

By way of introduction, four preferred embodiments will be presented inthe present disclosure.

A first embodiment entails a Buckyball-shaped polyhedron having twelvepentagonal rotating elements and twenty hexagonal faces, each hexagonalface being subdivided into six triangular faces, three of these sixtriangular faces being part of three mobile elements while the otherthree of these six triangular faces being part of three rotatingelements. The quasi-tetrahedron shaped mobile elements are groupedaround each of the rotating elements in shifting sections of theBuckyball to thus provide a soccer-ball shaped shifting puzzle wherebymobile elements of one group can be interchanged with mobile elements ofother groups.

A second embodiment also entails a Buckyball-shaped polyhedron butfurther includes, on each of the hexagonal faces, superimposedpermutable sliding members that slide in grooves in the underlyinghexagonal faces to provide both shifting and sliding movements.

A third embodiment is a shifting spherical puzzle created by dissectinga sphere with cutting planes that are parallel to each of the twelvefaces of a guiding dodecahedron to generate twelve partially overlappingouter spherical sections, each centered about a respective sphericalrotating element. The resulting spherical puzzle thus has twelveconvexly curved pentagonal rotating elements each having five inwardlycurved sides for engaging five oblong mobile elements, each havingoutwardly curved sides. Between each adjacent pair of the oblong mobileelements are disposed one of five triangular spherical gap elements. Thefive oblong mobile elements and the interspersed spherical gap elementstogether constitute a group of mobile elements that orbits together inunison when their respective rotating element is rotated. With therotating element, the five oblong mobile elements and the five sphericalgap elements together constitute an outer spherical section of thesphere (i.e. a convexly shaped outer portion of the sphere having acircular base plane) that overlaps with each of the five adjacent outerspherical sections associated with each of the five adjacent rotatingelements. Since the mobile elements of one group are shared withadjacent groups, rotation of one group can cause mobile elements to beinterchanged with mobile elements of adjacent groups.

By analogy with the first and second embodiments, the fourth embodimentbuilds upon the third embodiment by adding sliding movement to thepre-existing shifting movement to further complicate the puzzle. In thefourth embodiment, in addition to the shifting of each group ofspherical mobile elements, the spherical rotating elements, thespherical mobile elements and the spherical gap elements are providedwith grooves to enable superimposed sliding elements to slide relativeto the underlying shifting spherical gap elements. The superimposedsliding elements include three quasi-oblong elements with outwardlycurved sides, three quasi-triangular gap elements and a centraltriangular cap element that together constitute a rotatable circularcluster.

Embodiment 1: The Shifting Buckyball Puzzle

The first preferred embodiment is shown in FIG. 1 to FIG. 8.

Reference is now made to FIG. 1. The guiding polyhedron used to createthis three-dimensional logical puzzle is a semiregular Buckyballpolyhedron having twelve pentagonal and twenty hexagonal faces.Bisecting planes such as a1-b1-c1-d1-e1 that are parallel to eachpentagonal face are used to divide the polyhedron. Each hexagonal facesuch as aa-bb-dd-ee-ff-gg with geometrical center cc is bisected. Thisdividing method results in three types of elements: (i) a concealedcenter element, (ii) twelve rotating elements 20, (iii) thirty mobileelements 30. Each mobile element 30 is connected to the puzzle by aretaining means, i.e. a fastener, fastener subassembly, retainer orother retaining mechanism that enables elements to be interchanged fromone group to another group by “shifting” (i.e. twisting or rotating) onegroup relative to the other groups. For the purposes of nomenclature, a“group” in this embodiment is constituted of one rotating element 20 andfive mobile elements 30. Each rotating element 20 has five outer faces202 shaped like equilateral triangles such as face aa-cc-gg which formspart of one of the bisected hexagonal faces. Each rotating elementincludes means for retaining the pieces in an interfitting relationshipto thus enable rotational movement parallel to the bisecting planesalong rotating axes like axis a. Every mobile element 30 is effectivelyshared among its adjacent groups. Each mobile element 30 has two outerfaces 301 and 302 which are also part of the adjacent bisected faces.Vertices c1 and d1 are coincident with vertices bb and ff when the groupis in its initial non-rotated position, and non-coincident whenpartially rotated as illustrated in FIG. 1.

The center, rotating and mobile elements will now be describedindividually. The center element, located inside of the polyhedronpuzzle, can be either (a) an inner sphere, or (b) an internal concentricregular polyhedron, or (c) an axial rod (pivot) system, the latter beingillustrated in FIG. 2.

Reference is now made to FIG. 2 showing the center element 10. Thiscenter element 10 includes opposed extensions 11 and 12 extendingradially from the center of the polyhedron and aligned on axis a whichis one of the six non-orthogonal axes of the center element 10 disposedas in a regular dodecahedron for a total of twelve extensions. Eachextension has faces like face 101 parallel with every bisecting plane.At the tip or end of each extension is a bore or other mounting means 13for pivotally securing each respective rotating element 20. Again, whilethe center element is illustrated as a dodecahedronal axial rod system,it should be apparent that the center element could be constructed froma central polyhedron or a sphere without having an axial rod system.Center elements constructed in this fashion are within the scope of thepresent invention. Depending on the guiding polyhedron and the selecteddividing planes, the center element may or may not have exposed faces.

Reference is now made to FIG. 3. The illustrated rotating element 20 isshaped like an angularly extruded pentagon with a protrusion 21. Thisprotrusion 21 is used to place the rotating element 20 at an exactdistance from the geometrical center of the polyhedron. Each outwardface (or outer surface) 201 corresponds with one of the twelvepentagonal faces of the Buckyball polyhedron. Each surface 201 isprovided with a bore or other such holding means 22 for pivotallyholding the rotating element 20 on the center element 10. This bore orother holding means 22 is situated at the geometrical center of surface201, and is thus concentric and coincident with a respective axis ofrotation of the rotating element relative to the center element 10. Thefive outward faces 202 associated with each respective rotating element20 are shaped as equilateral triangles similar to aa-cc-gg and are partof five of the twenty bisected hexagonal faces forming the remainingfaces of the Buckyball polyhedron. An underside surface 205 is coplanarand coincident with the bisecting plane associated with the surface 201.Faces 203 of rotating element 20 are obtained from adjacent bisectingplanes slicing through the polyhedron. Arcuate faces 204 are provided tohold or retain the mobile elements 30.

Reference is now made to FIG. 4 which depicts a cross section of arotating element 20 taken along line b-b of FIG. 3. This cross sectionprovides a better view of the underside surface 205, while illustratinga mounting means for pivotally mounting each rotating element 20 on oneof the center element axial extensions. This mounting means isintegrated in each rotating element 20 by two countersunk bores 22 and24 terminated respectively by faces 23 and 207, each having a commoncenter hole passing therethrough. Face 207 is intended to rotate freelyover face 101. Bore 24 centers rotating element 20 on one of the sixaxes of the center element 10. Face 206 is only used to illustrate thecross-sectional view along line b-b and for some further references.

Reference is now made to FIG. 5. This figure depicts that mobileelements 30 are shaped like opposed quasi-tetrahedrons with outwardequilateral triangular faces 301 and 302 (which are similar to triangleaa-bb-cc) which are exposed and part of one of the bisected hexagonalfaces. The mobile element 30 is provided with a protrusion 31. Thisprotrusion 31 is a simple holding means for holding the mobile elements30 in an interfitting relationship with each respective rotating element20. Faces 305 and 306 are concentric with faces 204 of the two adjacentrotating elements 20. Protrusion 31 is terminated by face 307 and istapered to positively lock the mobile elements 30 to the adjacentrotating elements 20, thus securing the mobile elements 30 to the puzzleand enabling rotation and exchange of mobile elements 30 from a groupassociated with one rotating element 20 to another group associated witha different rotating element. Faces 303 and 304 are obtained by dividingthe base polyhedron with adjacent bisecting planes.

Reference is now made to FIG. 6 showing rotating elements 20 assembledon center element 10 plus a cross-section of a group constituted of asingle rotating element 20 and five mobile elements 30 with only halfbeing shown in the cross section. The cross section of this group isrepresented by a cross section of the rotating element 20 referenced byface 206 as in FIG. 4, two visible mobile elements 30 and one sectionedmobile element 30 along line aa-bb of FIG. 5 referenced by face 308. Inthis cross-sectional view, two mobile elements 30 are removed from thegroup to show one connecting means. This connecting means, which is usedfor pivotally interconnecting the protrusion 21 of each respectiverotating element 20 on center element 10, preferably includes a screw50, two washers 60 and a coil spring 70. The recessed bores of therotating elements 20 enable insertion of screws 50 from outside thepuzzle through the common hole to fasten the rotating elements 20 to thecenter element 10. These interconnecting means advantageously allow therotating elements 20 to rotate about their respective axis. The coilspring 70 located between the screw head 50 and the bottom of therecessed bore in between two optional washers 60 reduces frictiongenerated between adjoining surfaces and provides easily movableelements that are not prone to jamming, catching or getting hung up. Itshould be understood by those of ordinary skill in the art that theinterconnecting means could be replaced by snapping-action parts, whichwould also fall within the scope of the present invention. FIG. 6 alsoillustrates how the mobile elements 30 are taper locked onto respectiveadjacent rotating elements 20 through faces 204. These interconnectionsof the mobile elements 30 with the rotating elements 20 provide rotationabout the non-orthogonal axes and interfitting of elements 20 and 30 forenabling the interchanging of mobile elements 30 among differentadjoining groups. Also illustrated in FIG. 6 is the relation betweenbisecting planes like a1-b1-c1-d1-e1 and faces 203 and 205.

Reference is now made to FIG. 7. This figure illustrates the dividingmethod for obtaining the rotating elements 20 and mobile elements 30. Asmentioned previously, first divisions of the polyhedron are made withbisecting planes parallel to every pentagonal face of the Buckyball. Bydoing so, the Buckyball is sliced or cut along twelve planes equivalentto a1-b1-c1-d1-e1 producing twelve rotating elements 20 and also thirtymobile elements 30. This result is obtained if planes likea1-b1-c1-d1-e1 are coincident with their respective vertices situated atthe junction of every two of the bisected hexagonal faces and everypentagonal face. Different positions of the bisecting planes wouldresult in different types, forms and numbers of elements, all within thescope of the present invention. Faces 201, 202 and 205 in this firstpreferred embodiment are fully determined by these first divisionsthrough bisecting planes. Faces 203 and 204 are completed through seconddivisions by cutting a cylindrically shaped bore as shown. The radius Rof these cylinders is selected so that the circles described by radius Rat the intersections with hidden pentagonal faces like a1-b1-c1-d1-e1are fully inscribed within those pentagons. Provision is made withrespect to the radial dimension R for a wall thickness along line cc-cl.These second divisions enable interfitting of mobile elements 30 withrotating elements 20 through arcuate guiding taper faces that enable themobile elements to be slidingly engaged with the rotating elements.These interfittings securely hold mobile elements 30 to the puzzle whileenabling selective rotation of mobile elements 30 and respectiverotating elements 20 in groups along the inscribed circles, thusenabling a user of the puzzle to exchange or interchange mobile elements30 from group to group.

Reference is now made to FIG. 8. This figure further illustrates theinterfitting of one mobile element 30 with two adjacent rotatingelements 20 mounted on a center element 10. As shown, two adjacentbisecting planes divide part of the polyhedron, thus resulting in twofaces 203 and one mobile element 30 having a visible triangular face 301corresponding to equilateral triangle aa-bb-cc and a hidden triangularface 302. Faces 303 and 304 of mobile element 30 are coplanar andcontiguous with the two faces 203. Faces 305 and 306 of the protrusion31 are concentric and contiguous with adjacent arcuate faces 204. Theangle formed by faces 203 and 204 is such that mobile element 30 cannotslide out of its fitted position, thus preventing disassembly. Rotationof rotating element 20 around axis a will move mobile element 30 freelyin circles, thus displacing mobile element 30 into an adjacent group.Other interfittings, mechanisms or locking means are possible to allowfor interfitting and rotational movement between rotating elements 20and mobile elements 30. For example, locking means could include atongue and a groove mechanism, all within the scope of the presentinvention.

Embodiment 2: Shifting and Sliding Buckyball Puzzle

FIG. 9 to FIG. 13 illustrate a second preferred embodiment of theinvention, which is a three-dimensional logical puzzle also based on aBuckyball polyhedron. In addition to the rotational “shifting” movementdescribed with regard to the first embodiment (i.e. rotation of rotatingelements with their associated groups of mobile elements), this secondembodiment also provides for rotational “sliding” movement (i.e.rotation of clusters of superimposed elements that slide in groovesformed in the underlying mobile elements and rotating elements of thepuzzle).

Reference is now made to FIG. 9 showing a partial cross-sectional viewof a rotating element 20′ that is similar to the rotating element 20 butfurther incorporating an arcuate groove 25 on each triangular aa-cc-ggface 202 centered on every vertex cc. In this preferred embodiment thegroove is dovetail-shaped 26. It is understood that this groove could bemale (protrusion) or female (cavity), and of other shapes like L-shapedor T-shaped or of any shape that provides a retaining means allowingrotation about an axis perpendicular to face 202 and passing throughvertex cc. Vertex cc is the geometrical center of the bisected hexagonalface.

Reference is now made to FIG. 10 showing a concealed (i.e. hidden or“invisible”) mobile element 30′ similar to the mobile element 30 butfurther incorporating two arcuate retaining grooves 32, one on each ofits outer faces 301 and 302. These arcuate retaining grooves 32 areconcentric to their respective base vertices cc (each vertex cc beingthe geometrical center of its respective bisected hexagonal face). Inthis preferred embodiment, the grooves 32 are also dovetail-shaped 33like the dovetail-shape 26 of the groove 25 in the rotating element 20′.Different groove shapes can be substituted (e.g. T-shaped, L-shaped,etc.) as was the case with the groove of the rotating element 20′.

Reference is now made to FIG. 11. This figure introduces an optionalfourth “sliding” element 40 shaped as an angularly extruded equilateraltriangle having four outer faces 401, 402, 403 and 404. A protrusion 41having a dovetail shape 407 similar to groove shapes 26 and 33 isprovided to engage grooves 25 and 32. The shapes of the protrusion andgrooves can be varied (L-shaped, T-shaped, etc.) as was the case for therotating element 20′ and the concealed mobile element 30′. In thispreferred embodiment, the protrusion 41 extends underneath planeaa-bb-cc and acts as a guiding tongue. Both faces 405 and 406 areconcentric with vertex cc and slideably retain in the grooves 25 and 32the sliding element 40 with either the rotating element 20′ and/or theconcealed mobile element 30′. This mechanism enables sliding element 40to slide in the grooves in a curved (circular) path, to thus enable acluster of such elements 40 to effectively rotate about the geometricalcenter of the cluster. In other words, each superimposed sliding element40 slides in a curved track (the adjoining grooves) over the outer facesof the rotating elements 20′ and of the concealed mobile elements 30′along a circular slideway groove formed by adjacent grooves 25 and 32.In other words, this tongue-and-groove locking mechanism enables slidingelement 40, rotating element 20′ and mobile element 30′ to interfit insliding engagement with each other to enable curved “sliding” movementby which a cluster of such sliding elements 40 can be rotated by slidingaround the circular slideway. Thus, by adding sliding elements 40 inthis second embodiment, a puzzle of increased complexity is created thatcombines both shifting and sliding movements in a single polyhedralpuzzle. Although the foregoing represents best mode of implementing thesecond embodiment of this puzzle, it should be understood by those ofordinary skill in the art that other locking and sliding mechanisms canbe utilized or substituted in order to achieve similar results, all ofwhich lie within the scope of this invention.

Reference is now made to FIG. 12 to better illustrate the slidingactions added to the shifting puzzle in this second embodiment of theinvention. This figure illustrates a partially assembled puzzle inaccordance with the second preferred embodiment, depicting an explodedview of a cluster of sliding elements 40. A “cluster” is constituted ofsix equilateral triangular sliding elements 40 entirely or partiallycovering all or a subset of the bisected hexagonal facesaa-bb-dd-ee-ff-gg of the Buckyball puzzle. This cluster can be pivotedaround the geometrical center point cc, thus interchanging slidingelements 40 from one “augmented” group to another augmented group,thereby greatly increasing the difficulty level of the puzzle. An“augmented group” is constituted of a rotating element and a group ofmobile elements upon which are superimposed or carried half clusters ofsliding elements 40. Therefore, a complete Buckyball puzzle has twentyclusters for a total of one hundred and twenty (120) sliding elements40. FIG. 12 shows that grooves 25 and 32 form a smooth circular slidewayfor sliding rotational movements of the cluster of sliding elements 40to thus enable a user of the puzzle to interchange sliding elements fromone augmented group to another. The dovetail-shaped grooves prohibitsliding elements 40 from becoming disconnected from the puzzle. Faces401, 402 and 403 are cut to be coplanar with their respective restingpositions adjacent pentagonal faces and their respective adjacentbisecting planes. This prevents interference between elements whenaugmented groups are rotated.

Reference is now made to FIG. 13, which is an isometric view of theBuckyball puzzle in accordance with the second preferred embodiment ofthe present invention wherein one of the augmented groups has beenpartially rotated to a position between resting positions. Thisaugmented group is positioned outwardly of pentagonal facea1-b1-c1-d1-e1 as would be a (non-augmented) group in the firstpreferred embodiment. In addition to the five concealed mobile elements30′, however, the augmented group also displaces fifteen slidingelements 40. The entire Buckyball puzzle of the second preferredembodiment is thus covered by one hundred and twenty sliding elements40. Sliding elements 40 can now be exchanged from augmented group toaugmented group (in pure shifting movement) and also permuted withineach cluster of sliding elements (in superimposed sliding movement).These two types of movement combine to produce a potentially enormousnumber of permutations for the puzzle.

Reference is now made to FIG. 14 which shows possible physical locationsof visual indicia patterns (e.g. colors, logos, emblems, symbols, etc.)used to modulate the difficulty level of the puzzle. There are sevenindicia locations identified from L1 to L7 gathered inside a six-pointedinner hexagon star layout pattern. This layout pattern can be repeatedfor all or a subset of every hexagonal face of the puzzle, thusrequiring a total of thirty-two different indicia to make use of thefull potential of the puzzle. It is to be understood that the number ofvisual indicia used can be other than thirty two. These indicia could bemade of distinctive colors, textures, visible legends (numbers, letters,symbols, images, or a combination) or a combination of the above appliedon the visible portions of the puzzle. Indicia patterns are used toimpose challenges to the user of the puzzle in reconstituting apredetermined pattern and others. Proper selection of patterns andnumber of indicia modulates the difficulty level of the puzzle fromnovice to expert without any other modification to any of theconstituting elements. All the indicia pattern principles introducedhere can be applied to the first preferred embodiment of this inventionwith proper adjustments. For a basic level puzzle each hexagonal face inthe first preferred embodiment could simply be attributed a specificcolor (or other visual indicium).

Reference is now made to FIG. 15, illustrating an example of a visualindicia pattern for a novice-level puzzle in accordance with the secondpreferred embodiment. The visual indicia pattern for this novice-levelpuzzle is equivalent to the basic puzzle of the first preferredembodiment with the exception that there are one hundred and twentysliding elements 40 instead of merely thirty mobile elements 30 to berepositioned. In the pattern of this novice-level puzzle, a cluster isconstituted of six sliding elements 40 identified by one visualindicium, e.g. a single color, emblem, logo or symbol. In order to solvea shuffled novice-level puzzle, each cluster must be reassembled, butwithout any regard to the relative positioning among the clusters. Theadded number of sliding elements increases the difficulty level of thenovice puzzle compared to a basic level puzzle. In this novice patternno specific position is imposed on any sliding element 40 within acluster.

Reference is now made to FIG. 16 which depicts an example of a visualindicia pattern for an intermediate level puzzle in accordance with thesecond preferred embodiment. By adding unique positioning indicia on thepentagonal faces 201, the challenge becomes not only to reassemble eachone of the clusters (by reuniting the six sliding elements of like coloror indicium) but also to orient the cluster to concord with one of theunique positioning indicia depicted on the side of the pentagonalrotating element, as shown in FIG. 16. Thus, the difficulty level is nowmuch greater. However, any sliding element 40, being a member of acluster, can be positioned anywhere in the cluster.

Reference is now made to FIG. 17. This figure depicts an example of avisual indicia pattern for an expert level puzzle in accordance with thesecond preferred embodiment. Only one possible solution exists for thisexpert puzzle because visual indicia are displayed on both thepentagonal faces 201 of the rotating element 20′ and the faces 403 ofthe sliding elements 40. Thus, the one hundred and twenty (120) slidingelements 40 must be returned to a unique position in order to solve ashuffled puzzle. As will be appreciated, the number of permutations isastronomically large, thus providing a potentially very difficult puzzleto solve. However, a simplified, yet still challenging version of thepuzzle, can be made by modulating the visual indicia pattern so that thepuzzle can be solved by puzzle enthusiasts within a reasonable time.

By way of partial summary thus far, and without limiting the foregoingdiscussion, the first and second embodiments of the present inventionare based on the Buckyball-shaped polyhedron, i.e. a polyhedron that isshaped approximately like a soccer ball in which there are twelvepentagons and twenty hexagons (each hexagon being divided into sixtriangles).

The Buckyball polyhedron used in the first and second preferredembodiments is defined as a semiregular polyhedron, with thirty twofaces, twelve pentagons and twenty hexagons, ninety edges and sixtyvertices, exactly three edges emanating from each vertex (tri-valent),and all edges being of equal length.

The resulting Buckyball puzzle includes:

(i) A center element (or core) having six axes passing through thecenter of the puzzle and the geometrical center of every pair ofopposite pentagonal faces of an imaginary, or real, central regulardodecahedron polyhedron;

(ii) Twelve rotating elements shaped generally like an angularlyextruded pentagon rotationally mounted on the center element to providea plane of rotation for these elements parallel to their pentagonalouter faces;

(iii) Thirty mobile elements shaped like opposed quasi-tetrahedronsattached to the puzzle in groups of five around each rotating elementwith proper guiding surfaces enabling the mobile elements to change fromone group to another when the rotating elements are rotated; and

(iv) Optionally, one hundred and twenty sliding elements shapedgenerally like angularly extruded equilateral triangles guided andsecured in coincident semi-circular retaining groves provided in bothrotating and mobile elements, thus constituting hexagonal clusters ofsix permutable sliding elements superimposed on every hexagonal face ofthe puzzle.

Accordingly, the puzzle provides a plurality of rotating elements and aplurality of shiftable elements which rotate in groups and whichoptionally (in the second embodiment) combine superimposed slidingelements. The objective of these puzzles is to exchange or interchangemobile or sliding elements from group to group, or cluster to cluster,in order to restore the surfaces to their original pattern. Thedifficulty level of a single puzzle can be modulated by varying theindicia patterns situated on exposed faces of the polyhedron.

Although the first and second preferred embodiments are based on theBuckyball polyhedron, other semiregular polyhedrons could also be usedas the guiding polyhedron and bisected with the same dividing method,all without departing from the scope of the present invention. Likewise,the dividing method could also be applied to irregular polyhedrons toachieve create other interesting and challenging puzzles. Accordingly,the drawings and description are to be regarded as being illustrative,not as restrictive. In other words, these embodiments can be generalizedas being polyhedron-based puzzles having at least two different types offaces and to which a dividing method is applied that uses bisecting(also known as dissecting or cutting) planes that are parallel to one ofthe two faces, thus excluding at least one type of face (the “excludedfaces”). The excluded faces are divided by the bisecting planes togenerate a plurality of mobile elements while the non-bisected facesprovide a plurality of rotating elements.

Different positions of the bisecting planes in respect to the basepolyhedron vertices using the same proposed dividing method will resultin a different quantity of elements and a different type of elementsachieving either simpler or more complex puzzles. These simpler or morecomplex puzzles are within the scope of the invention presented in thisdisclosure. Various combinations, changes or modifications are possiblegiving almost any arbitrary exterior shape if the dividing method isused with other semiregular and irregular polyhedrons.

While the puzzle elements and parts are preferably manufactured fromplastic, these puzzles can also be made of wood, metal, or a combinationof the aforementioned materials. These elements and parts may be solidor hollow. The motion of the puzzle mechanism can be enhanced byemploying springs, bearings, semi-spherical surface knobs, grooves,indentations and recesses, as is well known in the art and are alreadywell described in the prior art of shifting and sliding puzzles.Likewise, “stabilizing” parts can also be inserted in the mechanism tobias the moving elements to the “rest positions”, as is also well knownin the art.

Embodiment 3: Shifting Spherical Puzzle

The third preferred embodiment is shown in FIG. 18 to FIG. 21.

Reference is now made to FIG. 18. The illustrated spherical rotatingelement 120 is obtained with the same dividing method as previouslymentioned except that the divided polyhedron is now replaced by a spherewith its radius selected to be coincident with vertex aa and gg of FIG.3. The spherical rotating element 120 is shaped like a convex pentagonwith a protrusion 121 performing the same function as the protrusion 21of the rotating element 20 shown in FIG. 3. The protrusion 121 isprovided with a holding means (not shown) for holding pivotally therotating element 120 on a half center core element 110. This holdingmeans is situated at the geometrical center of the protrusion 121 and isintended to be pivotally retained from within the puzzle without passingthrough the outer surface 1201 of the spherical rotating element 120.With suitable modification, the spherical rotating element 120 could beassembled on the center element 10, all within the scope of the presentinvention. As will be explained below, the center element 10 is optionalfor the spherical puzzle, i.e. the spherical puzzle can be designed withor without a center element or core. The outward face 1201 is a portionof the puzzle spherical outer shell and corresponds to a combination offace 201 and face 202. Faces 1203 and 1204 are similar to faces 203 and204 and perform the same functions.

Reference is now made to FIG. 19. This figure depicts a spherical mobileelement 130 similar to the mobile element 30 of FIG. 5. The outer face1301 also constitutes a portion of the puzzle's spherical outer shell.Protrusion 131, faces 1304, 1306 and 1307 are equivalent to theprotrusion 31, faces 304, 306 and 307. Faces 1309 and 1310 provideexactly the same functions as, respectively, faces 304 and 306 whilefurthermore acting to retain a spherical gap element 180, depicted inFIG. 20 and whose structure and function will be described below.

Reference is now made to FIG. 20. This figure shows a spherical gapelement 180 shaped like an equilateral spherical triangle. The outerface 1801 also forms part of the puzzle's spherical outer shell.Protrusion 181, faces 1802 and 1803 are functionally equivalent topreviously mentioned protrusion 131 and faces 1304, 1306. The sphericalgap element 180 is optionally cut along faces 1804 so that the elementsdo not interfere with each other when moved, i.e. the cutoff faces 1804ensure that elements of the spherical puzzle do not catch when they aredisplaced relative to one another.

Reference is now made to FIG. 21 showing a spherical puzzle inaccordance with the third preferred embodiment wherein one sphericalgroup is illustrated in an exploded view. This spherical group issimilar to the group defined above, including one spherical rotatingelement 120, five spherical mobile elements 130 (“first elements”) andfive spherical gap elements 180 (“second elements”). In all, thespherical puzzle in accordance with the third preferred embodiment isconstituted of two half center core elements 110 (shown in FIG. 23 andFIG. 24), twelve spherical rotating elements 120, thirty sphericalmobile elements 130 and twenty spherical gap elements 180. The puzzle inaccordance with the third preferred embodiment is completely spherical(thus aesthetically pleasing) and is believed to be slightly morecomplex than the Buckyball puzzle in accordance with the first preferredembodiment. As was the case wit the previous two embodiments, thisspherical puzzle is both challenging and entertaining. Furthermore, asdescribed above with regard to the first two embodiments, the difficultylevel of this puzzle can be modulated by varying the number of distinctcolours, emblems, logos or other visual indicia displayed on the outersurfaces of the elements of the puzzle.

Embodiment 4: Shifting and Sliding Spherical Puzzle

Reference is now made to FIG. 22. This figure illustrates a shifting andsliding spherical puzzle in accordance with a fourth preferredembodiment of the invention. The shifting motion of the puzzle isachieved by enabling augmented spherical group to move around modifiedspherical rotating elements 120′ while the sliding motion of the puzzleis achieved by enabling spherical clusters to move around spherical-gapcap elements 140. In this particular spherical puzzle, an augmentedspherical group includes one modified spherical rotating element 120′,five modified spherical mobile elements 143, ten spherical mobile capelements 141, five modified concealed spherical gap elements 180′, fivespherical-gap cap elements 140 and five spherical rotating cap elements142. All the previously mentioned modified elements 120′, 143, 180′incorporate modifications similar to the puzzle of the second preferredembodiment in order to enable sliding of superimposed elements in eachspherical cluster. These modifications are analogous to themodifications made to the first embodiment to create the secondembodiment, and therefore need not be repeated herein. In the fourthpreferred embodiment, a spherical cluster is constituted of onespherical-gap cap element 140, three spherical mobile cap elements 141and three spherical rotating cap elements 142. A complete puzzle of thefourth embodiment is constituted of two half center core elements 110(as shown in subsequent figures), twelve modified spherical rotatingelements 120′, thirty modified spherical mobile elements 143, twentymodified concealed spherical gap elements 180′, twenty spherical-gap capelements 140, sixty spherical mobile cap elements 141 and sixtyspherical rotating cap elements 142. All these cap elements areexchangeable from one augmented spherical group to another augmentedspherical group and within spherical clusters, thus providing apotentially huge number of permutations for the serious puzzleenthusiast seeking an ultimate puzzle challenge.

Reference is now made to FIG. 23. This figure illustrates theinterfitting and snapping action of two half center core elements 110.When assembled together these two half center core elements form ahollow center core element shaped as a regular dodecahedron.Similarities between this hollow center core element and the centerelement 10 are apparent from FIG. 2. Faces 111 and 1101 are equivalentto the extension 11 and face 101. The mounting means (e.g. the bore) 13is now implemented directly in the spherical rotating element 120 insideits protrusion 121 with a bore or other such mounting means 113 servingas a through hole for assembly. With this hollow center core elementthere is exactly six non-orthogonal axes as with the center element 10,axis a-a being one of them. As with the previous center elements thereare twelve mounting positions provided to receive twelve sphericalrotating elements 120 or 120′. This hollow center core element canreplace the center elements of the first and second preferredembodiments by making proper modifications to the rotating elements.These modifications lie within the scope of the present invention. Ingeneral, depending on the guiding polyhedron and the selected dividingplanes, the hollow center core element may or may not have exposedfaces. Snapping protrusions facing inside 114 and outside 115 areprovided to enable simple and firm assembly of two half center coreelements 110 to constitute the hollow center core element.

Reference is now made to FIG. 24. This figure shows a mechanism forinternally interconnecting the spherical rotating elements 120 or 120′to the two half center core elements 110. As depicted in FIG. 24, thespherical rotating elements 120 or 120′ are rotationally connected tothe hollow center core element by a screw 50, two (optional) washers 60and a coil spring 70. Each screw 50 is inserted from inside the puzzlethrough the bores 113 to fasten the respective spherical rotatingelement 120 or 120′ to the half center core elements 110. No recessedbores are required on the outside surfaces of the spherical rotatingelements 120 or 120′ and thus no capping of elements is required inorder to obtain an even and smooth outer surface over the sphericalouter shell of the puzzle. This design can also be implemented in thefirst and second embodiments by also using a hollow center core element.FIG. 21 and FIG. 22 illustrate the even and smooth outer shell of thepuzzles in accordance with the third and fourth embodiments. It isunderstood that the interconnecting mechanism could be replaced bysnapping action parts, all within the scope of the present invention.

As mentioned above, the spherical puzzles of the third and fourthembodiment can also be constructed without a core or center element 10.While it is preferable to utilize a core or center element 10, it isalso possible to construct the spherical puzzles of the third and fourthembodiment without any core or center element 10. A coreless sphericalpuzzle can be constructed by providing the spherical rotating elements120, spherical mobile elements 130 and spherical gap elements 180 withappropriate protrusions and grooves. These protrusions and groovescooperate as interfitting male and female connections to slideably androtatably interlock the various elements to thus hold the elementstogether to form a complete sphere. Since the spherical rotatingelements 120, spherical mobile elements 130 and spherical gap elements180 are interlocked, there is no longer any need for a center element 10or core to retain or hold the various elements of the spherical puzzlein place. For example, in one implementation of this coreless sphericalpuzzle, each spherical rotating element 120 would have grooves (orfemale connectors) on each of its five inwardly curved sides. Tointerlock with each spherical rotating element 120, each sphericalmobile element 130 would have protrusions (male connectors) on its twooutwardly curved sides with grooves (female connectors) on its twoinwardly curved sides. To interlock with both the spherical rotatingelements 120 and the “female sides” of the spherical mobile elements130, each of the spherical gap elements 180 would have protrusions (ormale connectors) on each of its three sides.

The same techniques for arranging the display of colours, emblems, logosor other visual indicia on the outer surfaces of the puzzles to modulatethe difficulty level (as was described with regard to FIGS. 14-17) arealso applicable, with minor modifications, to both the third and fourthpreferred embodiments. However, with spherical puzzles, the difficultylevel for a particular indicia pattern will generally be higher due tothe added number of elements involved, particular for the fourthpreferred embodiment with its one hundred and eighty-two outer elements.More complex indicia patterns can be developed to impose a uniquesolution on every outer element. Complex descriptions of evolutedpatterns are not included in the present disclosure for the sake ofsimplicity, but are well within the scope of the technology introducedhere and can be easily derived from the principles already disclosed.Generally, though, the indicia patterns are used to modulate the puzzledifficulty level by changing the total number of permutations to makethe puzzle reasonably solvable.

The visual indicia could be made of distinctive colours, textures,visible legends (numbers, letters, symbols, images, or a combination) ora combination of the above, or patterns of the above, or corporateand/or team logos, or emblems, or national flags applied on the visibleportions of the puzzle. The outer shell of the puzzles can be used tomimic objects such as a soccer ball, basketball, baseball or the like.The outer shell could reproduce cartoons, heads and/or faces, organs,planets and the like. The outer shell could be used for learningpurposes, publicity and marketing purposes, artistic purposes and otherapplications as well.

In a variant, some or all of the hexagonal faces can be made pyramidal,i.e. the geometrical centers of the hexagonal faces can be stellated.The resulting stellated puzzle would have a spiky appearance.

It will be noted that exact dimensions are not provided in the presentdescription since these puzzles can be constructed in a variety ofsizes.

The foregoing puzzles are symmetrical, aesthetically-pleasing,entertaining and challenging. Although the theoretical number ofpermutations is enormous, especially for the second and fourthembodiments, the difficulty level of these puzzles can be easilymodulated by reducing the number of different visual indicia (e.g. colorschemes or face patterns) that are displayed on the faces. In otherwords, different versions of the puzzle can be provided for novice,intermediate or expert players, or even for kids.

Three-Dimensional Puzzles Having Outer Element Surfaces DisplayingCorporate and/or Team Logos

Another aspect of the present invention is a three-dimensional puzzlethat serves as an advertising medium. In other words, thisthree-dimensional logical puzzle includes a plurality of moving elementshaving outer surfaces upon which can be displayed one or more logos suchas, for example, corporate logos or sports team logos.

The puzzle is preferably either a Buckyball-shaped puzzle or a sphericalpuzzle, but other shapes could be used for displaying corporate or teamlogos. For example, since the Buckyball approximately resembles a soccerball, the Buckyball-shaped puzzle is ideally suited as a promotionalitem in the world of soccer. For example, since the Buckyball-shapedpuzzle has 32 faces (12 pentagons and 20 hexagons), the Buckyball puzzlewould be ideally suited to display the national soccer team logo of eachof the 32 nations in the FIFA World Cup Soccer Tournament. Of course,the puzzle can be used to display team logos for other tournaments orleagues having fewer than 32 teams (by simply leaving some surfacesblank or by using one or more of these “spare” surfaces to identify theleague or authority (e.g. FIFA, UEFA, English Premier League) or toidentify the host country, year of the tournament, etc.)

Again by way of example only, the faces of the Buckyball could alsodisplay corporate logos of sponsors of a tournament or event. Forexample, the logos of each of the corporate sponsors (Yahoo®,Coca-Cola®, Mastercard®, etc.) of the FIFA World Cup tournament could bedisplayed on each of the outer faces of the Buckyball puzzle.Alternatively, the puzzle could display a mix of team and corporatelogos. Alternatively, only a subset of the outer faces of the puzzlecould display logos, with the other surfaces being blank or solidcoloured (i.e. to reduce the difficulty level of the puzzle, e.g. forkids).

As other examples, all or a subset of the faces of the Buckyball puzzlecould be used to display team logos for the various teams of nationalsoccer leagues, such as the English Premier Division, the Italian SerieA, the German Bundesliga, etc. As further examples, the Buckyball puzzlecould display player jerseys (with player names and/or numbers), playerfaces, league emblems, etc. In addition to the Buckyball puzzle, thespherical puzzle is also ideally suited for corporate advertising orteam logos in the world of soccer due to its close resemblance to asoccer ball.

Using the puzzles for advertising or displaying team or corporate logoscan of course be utilized in other sports, including, but not limitedto, basketball, baseball, tennis, golf, volleyball, handball, waterpolo, etc. where the puzzle can be made to mimic the look of the actualball, for example, by drawing or printing suitable seams, lines,dimples, etc. on the outer surfaces of the puzzle to create a replica ofthe actual ball. For example, a puzzle made to look like a baseballcould have seams drawn over the outer surfaces, with major league teamlogos or emblems on each of the outer surfaces, or on a subset of theouter surfaces.

Although the spherical puzzle is best suited for producing replica ballsfor sports having round balls, the same concept can be applied to sportsthat do not involve balls, or to sports having differently shaped balls(regardless whether the shape of the puzzle matches the shape of theactual ball used) such as, for example, for hockey, football, rugby,boxing, motor sports, etc.

In the foregoing examples, it should be noted that the difficulty-levelof the puzzles could be modulated by displaying fewer logos on thepuzzle, with some faces being solid colours or blank (white) forexample, or by displaying logos that cover more than one of the outersurfaces of the puzzle. A very simple Buckyball or spherical puzzlewould thus have two solid coloured hemispheres. By analogy, a logopuzzle having only two large logos, one on each of the hemispheres,would be fairly easy to solve. Alternatively, a single corporate sponsorcould advertise exclusively on a spherical puzzle or Buckyball puzzle byhaving multiple instances of their emblem, for example, interspersedwith solid colours (or white surfaces), or alternatively, have a singlecorporate emblem or logo printed on the entire outer surface such thatit is effectively “wrapped around” the entire sphere or Buckyball.

Thus, it should be apparent that the logos need not be confined to eachhexagonal or pentagonal surface of the Buckyball, e.g. a logo could bedisplayed over two or more contiguous outer faces. In the case of thespherical puzzle, the logos or other visual indicia could be printedwithout discretely confining the displays to each cluster of elements.Thus, for example, one could also produce a spherical puzzle having amap, stylized map or satellite photo of Planet Earth, of the moon, or ofanother planet, of a head of a person (historical, celebrity, famous orotherwise), or any other pattern of colors, artwork, photo, etc. thatwould provide an interesting visual puzzle.

In another example, a spherical or Buckyball puzzle could havealternating black and white faces like a traditional soccer ball butupon which a small number of logos would be displayed. Again, thedifficulty level of the puzzle can be modulated by changing the numberand size of the logos. A replica of the official ball of the FIFA WorldCup or of a particular team or league or tournament or event could becreated. For example, for fans of the Azzurri, a puzzle replicating ablue soccer ball with the colours and emblems of the Italian nationalsoccer team could be produced, e.g. with the red, white and greenItalian flag placed on one or more faces of the ball. For example, forfans of Manchester United, a puzzle replicating a red ball could beproduced with the team emblem on one or more faces.

The puzzle with logos would provide not only a useful advertising mediumfor corporate sponsors, but also serve as entertainment for fans beforethe game, during half-time, or afterwards. In addition to being achallenging and fun toy, the puzzle displaying team logos, playerjerseys, player faces, etc. would also serve as a lasting souvenir ormemento of a particular tournament for fans to cherish for many yearsafterwards, while providing highly valuable, ongoing advertising forcorporate sponsors, particularly for those puzzles that display a mix ofteam and corporate logos, for example, the emblems of the two finalistsof a major tournament or league plus the corporate names/logos of thetournament's primary sponsors.

Although the preferred embodiments are the Buckyball puzzle and thespherical puzzle, it should be noted that advertising, corporate logosor team logos could also be placed onto the surfaces of other types ofthree dimensional puzzles to create promotional vehicles or souvenirs.

It is understood that the above description of the preferred embodimentsis not intended to limit the scope of the present invention, which isdefined solely by the appended claims.

1. A three-dimensional semiregular or irregular polyhedron-based logicalpuzzle having at least two different types of outer faces, the puzzlecreated by a dividing method requiring that bisecting planes parallel tothe faces be chosen to exclude at least one type of face, thus definingexcluded faces, the puzzle comprising at least three types of elements:(a) a center element having at least six non-orthogonal axes passingthrough the geometrical center of some or all of the outer faces of thepolyhedron and passing through the geometrical center of the puzzle, butwithout passing through the excluded faces; (b) a plurality of rotatingelements rotationally connected to the center element, the rotatingelements obtained through the bisecting planes used to slice the basepolyhedron on every outside face corresponding to the axes; and (c) aplurality of mobile elements obtained through the bisecting planesslicing the excluded faces, the mobile elements interfitting withadjacent rotating elements and/or mobile elements to prevent disassemblyof the puzzle and to enable one of the rotating elements and anassociated plurality of the mobile elements to rotate in a group aroundits respective axis, whereby rotation of the group enables a user tointerchange mobile elements between adjacent groups.
 2. The logicalpuzzle as claimed in claim 1 wherein the polyhedron is aBuckyball-shaped polyhedron having six pairs of opposed rotatingelements rotationally connected to the center element about sixnon-orthogonal axes, the Buckyball polyhedron having thirty-two facesincluding twelve pentagonal faces and twenty hexagonal faces, whereinthe puzzle comprises: (a) one center element with exactly six axespassing through the geometrical center of the puzzle and through thegeometrical center of each opposed pentagonal face; (b) twelve rotatingelements rotationally connected to the center element, the rotatingelements obtained through the bisecting planes used to slice theBuckyball-shaped polyhedron, the bisecting planes being parallel to eachof the pentagonal faces; (c) thirty mobile elements obtained through thebisecting planes slicing bisected hexagonal faces, the bisecting planespassing through the geometrical centers of the bisected hexagonal faces,the mobile elements interfitting with adjacent rotating elements toprevent disassembly of the puzzle and to enable one of the rotatingelements and five of the mobile elements to rotate as a group around itsrespective axis, whereby rotation of the group interchanges the mobileelement positions.
 3. The logical puzzle as claimed in claim 2 whereinthe center element is an axial rod system having six opposed extensionsextending radially outwardly from the center of the polyhedron inalignment with the geometrical centers of each pentagonal face of aninvisible regular central dodecahedron, thus providing a total of twelveextensions for rotationally connecting each of the twelve rotatingelements to the center element.
 4. The logical puzzle as claimed inclaim 2 wherein the center element is an inner core central elementformed by a central regular dodecahedron located at the geometric centerof the polyhedron-based puzzle having bores for rotationally connectingeach rotating element to the center element.
 5. The logical puzzle asclaimed in claim 4 wherein the inner core center element is formed bysnapping together two half dodecahedral elements having protrusionsfacing inwardly and outwardly for mating the half dodedahedral elementstogether.
 6. The logical puzzle as claimed in claim 2 wherein each ofthe rotating elements is shaped like an angularly extruded pentagoncomprising one outward face forming one of the twelve outer pentagonalsurfaces of the Buckyball polyhedron, the rotating element furthercomprising five obliquely angled triangular faces shaped as equilateraltriangles, forming part of five of twenty bisected hexagonal faces inthe puzzle.
 7. The logical puzzle as claimed in claim 6 wherein eachrotating element comprises a rotational mechanism having a screw, a coilspring, and at least one washer arranged within concentric bores, oneexternal bore being situated at the geometrical center of the pentagonalface and one internal bore situated in a protrusion, the internal boreserving to position the rotating element on the center elementconcentric with its respective axis, the bores dimensioned to provide adividing thickness between the bores to locate the rotating element atan exact distance from the geometrical center of the polyhedron.
 8. Thelogical puzzle as claimed in claim 6 wherein each rotating elementcomprises a rotational mechanism having a screw, a coil spring, and atleast one washer fixed to an internal bore situated at a geometricalcenter of a protrusion of each rotating element, the protrusion servingto position the rotating element on the center element concentric withits respective axis, and to locate the rotating element at an exactdistance from the geometrical center of the polyhedron.
 9. The logicalpuzzle as claimed in claim 6 wherein the rotating element comprises aplurality of concealed faces, each concealed face having an arcuate facethat cooperates with another arcuate face to define arcuate guidingtaper faces enabling sliding movement relative to a mobile element. 10.The logical puzzle as claimed in claim 2 wherein the mobile element isgenerally shaped like opposed quasi-tetrahedrons having two equilateraltriangular outer faces and two generally triangular concealed internalfaces coplanar with surfaces of the adjacent rotating elements.
 11. Thelogical puzzle as claimed in claim 10 wherein the mobile elementcomprises a tapered protrusion for interfitting the mobile element toadjacent rotating elements, thereby allowing rotation of the mobileelements with one of the adjacent rotating elements as a group around arotational axis of the rotating element.
 12. The logical puzzle asclaimed in claim 2 wherein the rotating elements and mobile elementsfurther comprise retaining grooves for enabling superimposed slidingelements to slide relative to the rotating elements and mobile elements.13. The logical puzzle as claimed in claim 12 comprising 120 slidingelements that are slidingly superimposed within grooves formed within 30concealed mobile elements and 12 rotating elements.
 14. The logicalpuzzle as claimed in claim 13 wherein the center element is an axial rodsystem having six opposed extensions extending radially outwardly fromthe center of the polyhedron in alignment with the geometrical centersof each pentagonal face of an invisible regular central dodecahedron,thus providing a total of twelve extensions for rotationally connectingeach of the twelve rotating elements to the center element.
 15. Thelogical puzzle as claimed in claim 13 wherein the center element is aninner core central element formed by a central regular dodecahedronlocated at the geometric center of the polyhedron-based puzzle havingbores for rotationally connecting each rotating element to the centerelement.
 16. The logical puzzle as claimed in claim 15 wherein the innercore center element is formed by snapping together two half dodecahedralelements having protrusions facing inwardly and outwardly for mating thehalf dodedahedral elements together.
 17. The logical puzzle as claimedin claim 13 wherein each of the rotating elements is shaped like anangularly extruded pentagon comprising one outward face forming one ofthe twelve outer pentagonal surfaces of the Buckyball polyhedron, therotating element further comprising five obliquely angled triangularfaces shaped as equilateral triangles, forming part of five of twentybisected hexagonal faces of the puzzle, arcuate retaining grooves beingformed in every equilateral triangular outer face of the rotatingelements for slidingly receiving superimposed sliding elements, thearcuate retaining grooves being concentric with a base vertex of theequilateral triangular outer face, thus guiding the sliding elements inrotation around the base vertex while securing the sliding elements tothe puzzle.
 18. The logical puzzle as claimed in claim 17 wherein eachrotating element comprises a rotational mechanism having a screw, a coilspring, and at least one washer arranged within concentric bores, oneexternal bore being situated at the geometrical center of the pentagonalface and one internal bore situated in a protrusion, the internal boreserving to position the rotating element on the center elementconcentric with its respective axis, the bores dimensioned to provide adividing thickness between the bores to locate the rotating element atan exact distance from the geometrical center of the polyhedron.
 19. Thelogical puzzle as claimed in claim 17 wherein each rotating elementcomprises a rotational mechanism having a screw, a coil spring, and atleast one washer fixed to an internal bore situated at a geometricalcenter of a protrusion of each rotating element, the protrusion servingto position the rotating element on the center element concentric withits respective axis, and to locate the rotating element at an exactdistance from the geometrical center of the polyhedron.
 20. The logicalpuzzle as claimed in claim 17 wherein the rotating element comprises aplurality of concealed faces, each concealed face having an arcuate facethat cooperates with another arcuate face to define arcuate guidingtaper faces enabling sliding movement relative to a concealed mobileelement.
 21. The logical puzzle as claimed in claim 13 wherein eachconcealed mobile element comprises opposed quasi-tetrahedrons having twoequilateral triangular concealed outer faces and two generallytriangular concealed internal faces coplanar with surfaces of theadjacent rotating elements, the triangular concealed outer faces havingarcuate semi-circular retaining grooves for sliding of the slidingelements concentrically with a base vertex of the equilateral triangularconcealed outer face, thus guiding the sliding elements in rotationaround the base vertex while securing the sliding elements to thepuzzle.
 22. The logical puzzle as claimed in claim 21 wherein theconcealed mobile element comprises a tapered protrusion for interfittingthe concealed mobile element to adjacent rotating elements, therebyallowing rotation of the mobile elements with one of the adjacentrotating elements as a group around a rotational axis of the rotatingelement.
 23. The logical puzzle as claimed in claim 13 wherein theconcealed mobile elements and the rotating elements comprise arcuateretaining grooves for slidingly receiving superimposed sliding elementsshaped as equilateral triangles arranged in clusters of six triangularsliding elements superimposed over each hexagonal face of the puzzle.24. The logical puzzle as claimed in claim 23 wherein the slidingelement comprises a protrusion at its base acting as a guiding tongue toengage the sliding elements in respective arcuate retaining grooves ofthe concealed mobile elements and of the rotating elements, the arcuateretaining grooves of the elements constituting one of the hexagonalfaces together forming a circular slideway to slideably connect eachsliding element for rotation as a cluster of six sliding elements, eachcircular slideway being concentric with a respective center vertex ofthe respective hexagonal face.
 25. A spherical puzzle created by cuttinga plurality of outer spherical sections from a sphere using cuttingplanes parallel to each of the faces of a guiding regular polyhedronhaving at least twelve faces, the puzzle comprising: i) a plurality ofrotating elements having a convex outer face defining a portion of asphere; ii) a plurality of first mobile elements connected to each ofthe rotating elements; iii) a plurality of second gap elements connectedto each of the rotating elements between each of the first mobileelements; whereby the rotating elements, the first mobile elements andthe second gap elements together constitute a complete sphere andwherein the rotating elements and their respective groups of first andsecond elements together define overlapping circles on the sphere toenable interchanging of first and second elements of one group withfirst and second elements of another adjacent group.
 26. The sphericalpuzzle as claimed in claim 25 further comprising a center elementdefining at least 6 axes, wherein the rotating elements are rotationallyconnected to the center element.
 27. The spherical puzzle as claimed inclaim 26 wherein the guiding regular polyhedron is a dodecahedron, thuscutting the sphere into twelve outer spherical sections that partiallyoverlap, the spherical puzzle thus comprising 12 spherical rotatingelements rotationally connected in opposed pairs to the center elementabout 6 axes, wherein the first mobile elements comprise 30 sphericalmobile elements adjacent to the spherical rotating elements, and whereinthe second gap elements comprise 20 spherical gap elements.
 28. Thelogical puzzle as claimed in claim 27 wherein the center element is anaxial rod system having six opposed extensions extending radiallyoutwardly from the center of the polyhedron in alignment with thegeometrical centers of each pentagonal face of an invisible regularcentral dodecahedron, thus providing a total of twelve extensions forrotationally connecting each of the twelve rotating elements to thecenter element.
 29. The logical puzzle as claimed in claim 27 whereinthe center element is an inner core central element formed by a centralregular dodecahedron located at the geometric center of thepolyhedron-based puzzle having bores for rotationally connecting eachrotating element to the center element.
 30. The logical puzzle asclaimed in claim 29 wherein the inner core center element is formed bysnapping together two half dodecahedral elements having protrusionsfacing inwardly and outwardly for mating the half dodedahedral elementstogether.
 31. The spherical puzzle as claimed in claim 27 wherein eachof the twelve outer spherical sections comprise a spherical rotatingelement rotationally connected to a center element and a group ofspherical mobile elements connected to the spherical rotating elementfor rotation in unison with the spherical rotating element, wherein eachspherical rotating element is a convexly curved pentagon.
 32. Thespherical puzzle as claimed in claim 31 wherein each spherical rotatingelement comprises a rotational mechanism having a screw, a coil spring,and at least one washer arranged within concentric bores, one externalbore being situated at the geometrical center of the convexly curvedpentagonal face and one internal bore situated in a protrusion, theinternal bore serving to position the spherical rotating element on thecenter element concentric with its respective axis, the boresdimensioned to provide a dividing thickness between the bores to locatethe spherical rotating element at an exact distance from the geometricalcenter of the spherical puzzle.
 33. The spherical puzzle as claimed inclaim 31 wherein each spherical rotating element comprises a rotationalmechanism having a screw, a coil spring, and at least one washer fixedto an internal bore situated at a geometrical center of a protrusion ofeach spherical rotating element, the protrusion serving to position thespherical rotating element on the center element concentric with itsrespective axis, and to locate the spherical rotating element at anexact distance from the geometrical center of the spherical puzzle. 34.The spherical puzzle as claimed in claim 31 wherein the sphericalrotating element comprises a plurality of concealed faces, eachconcealed face having an arcuate face that cooperates with anotherarcuate face to define arcuate guiding taper faces for interfittingspherical mobile elements and spherical gap elements.
 35. The sphericalpuzzle as claimed in claim 27 wherein the spherical mobile elementscomprise five convexly shaped generally oblong elements having outwardlycurved sides whereas the second gap elements comprise five generallyspherical triangular elements that occupy the generally triangular gapsbetween adjacent oblong elements.
 36. The spherical puzzle as claimed inclaim 35 wherein each spherical mobile element and each spherical gapelement comprises a tapered protrusion for rotational interfitting withadjacent spherical rotating elements, mobile elements and spherical gapelements.
 37. The spherical puzzle as claimed in claim 27 comprising onecenter element with exactly 6 axes; 12 modified spherical rotatingelements modified to have grooves therein; 30 modified spherical mobileelements modified to have grooves therein; 20 modified concealedspherical gap elements modified to rotationally support 20 spherical-gapcap elements; and 60 spherical rotating cap elements and 60 sphericalmobile cap elements having protrusions for engaging the grooves forsuperimposed sliding relative to the modified spherical rotatingelements, modified spherical mobile elements and modified concealedspherical gap elements.
 38. The spherical puzzle as claimed in claim 37wherein the center element is an axial rod system having six opposedextensions extending radially outwardly from the center of the sphericalpuzzle in alignment with the geometrical centers of each pentagonal faceof an invisible regular central dodecahedron, thus providing a total oftwelve extensions for rotationally connecting each of the twelvemodified spherical rotating elements to the center element.
 39. Thespherical puzzle as claimed in claim 37 wherein the center element is aninner core central element formed by a central regular dodecahedronlocated at the geometric center of the spherical puzzle having bores forrotationally connecting each modified spherical rotating element to thecenter element.
 40. The spherical puzzle as claimed in claim 39 whereinthe inner core center element is formed by snapping together two halfdodecahedral elements having protrusions facing inwardly and outwardlyfor mating the half dodedahedral elements together.
 41. The sphericalpuzzle as claimed in claim 37 wherein the modified spherical rotatingelements are convexly-shaped, generally pentagonal elements comprisingarcuate retaining grooves for receiving superimposed spherical slidingelements that slide in the grooves with respect to the modifiedspherical rotating elements, the arcuate retaining grooves in theconvexly-shaped outer faces being concentric with base vertices of theconvexly-shaped generally pentagonal outer face, thus guiding thesliding elements in rotation around the base vertices while securing thesliding elements to the puzzle.
 42. The spherical puzzle as claimed inclaim 41 wherein each modified spherical rotating element comprises arotational mechanism having a screw, a coil spring, and at least onewasher arranged within concentric bores, one external bore beingsituated at the geometrical center of the pentagonal face and oneinternal bore situated in a protrusion, the internal bore serving toposition the modified spherical rotating element on the center elementconcentric with its respective axis, the bores dimensioned to provide adividing thickness between the bores to locate the modified sphericalrotating element at an exact distance from the geometrical center of thespherical puzzle.
 43. The spherical puzzle as claimed in claim 41wherein each modified spherical rotating element comprises a rotationalmechanism having a screw, a coil spring, and at least one washer fixedto an internal bore situated at a geometrical center of a protrusion ofeach modified spherical rotating element, the protrusion serving toposition the modified spherical rotating element on the center elementconcentric with its respective axis, and to locate the modifiedspherical rotating element at an exact distance from the geometricalcenter of the spherical puzzle.
 44. The spherical puzzle as claimed inclaim 41 wherein the modified spherical rotating element comprises aplurality of concealed faces, each concealed face having an arcuate facethat cooperates with another arcuate face to define arcuate guidingtaper faces enabling interfitting with, and sliding movement relativeto, the modified spherical mobile elements and modified concealedspherical gap elements.
 45. The spherical puzzle as claimed in claim 37wherein the modified spherical mobile elements are convexly-shapedgenerally oblong elements having outwardly curved sides comprisingarcuate retaining groove for receiving superimposed spherical slidingelements that slide in the grooves with respect to the modifiedspherical mobile elements.
 46. The spherical puzzle as claimed in claim45 wherein each modified spherical mobile element comprises a taperedprotrusion for slidingly interfitting the modified spherical mobileelement with adjacent elements.
 47. The spherical puzzle as claimed inclaim 37 wherein each modified concealed spherical gap element isconvexly-shaped generally triangular, and wherein each modifiedconcealed spherical gap element rotationally supports a superimposedspherical gap-cap element about which a cluster of superimposedspherical sliding elements may be rotated.
 48. The spherical puzzle asclaimed in claim 47 wherein each modified concealed spherical gapelement comprises a tapered protrusion for slidingly interfitting themodified concealed spherical gap element with adjacent elements.
 49. Thespherical puzzle as claimed in claim 37 wherein each spherical gap-capelement is convexly-shaped generally triangular.
 50. The sphericalpuzzle as claimed in claim 49 wherein each spherical gap-cap elementcomprises a tapered protrusion for being rotationally mounted to arespective underlying modified concealed spherical gap element.
 51. Thespherical puzzle as claimed in claim 37 wherein each spherical rotatingcap element is convexly-shaped generally triangular having one curvedside defining a circular arc.
 52. The spherical puzzle as claimed inclaim 51 wherein each spherical rotating cap element comprises a taperedprotrusion for sliding engagement within a circular slideway defined bythe grooves of underlying elements.
 53. The spherical puzzle as claimedin claim 37 wherein each spherical mobile cap element is convexly-shapedgenerally oblong having one curved side defining a circular arc.
 54. Thespherical puzzle as claimed in claim 53 wherein each spherical mobilecap element comprises a tapered protrusion for sliding engagement withina circular slideway defined by the grooves of underlying elements. 55.The logical puzzle as claimed in claim 12 comprising a visual indiciapattern displayed on the outer surface of the elements of the puzzlewherein the pattern has seven indicia locations L1-L7 situated onexposed faces of the puzzle representing seven different visual indiciaS1-S7 and wherein the indicia pattern for the puzzle is generated basedon a layout shaped like a six-pointed inner hexagon star formed by oneinner hexagonal face, three uniformly distributed pentagonal star pointsbeing part of three adjacent pentagonal faces and three uniformlydistributed hexagonal star points being part of adjacent hexagonalfaces, each trapezoidal side face of the sliding elements situated atthe circumferential boundary of the inner hexagonal face being assigneda boundary indicia location symbol number from L2 to L7 starting with L2being assigned to a first trapezoidal side face located at thecircumferential boundary of the inner hexagonal face and one of thethree adjacent pentagonal faces, the remaining trapezoidal side facesbeing assigned boundary indicia location symbol numbers from L3 to L7,every other face included in the inner hexagonal faces being identifiedby an inner indicia location symbol number L1, the indicia pattern beingfurther generated by adding cross references identified by the boundaryindicia location symbol number L1 for all three of the pentagonal starpoints at locations closest to the circumferential boundary of the innerhexagonal face and three other L1 references on all trapezoidal sidefaces of the sliding elements contiguous with the circumferentialboundary of the inner hexagonal face and situated on all three of theadjacent hexagonal faces, the indicia pattern being completed byrepeating every boundary indicia location symbol number from L2 to L7 atthe tip of every respective pentagonal and hexagonal star points, theindicia pattern being repeated for all or a subset of the twentyhexagonal faces of the puzzle using all or a subset of the seven indicialocation symbol numbers L1 to L7 representing all or a subset of thethirty-two visual indicia S1 to S32 to be displayed on the puzzle. 56.The logical puzzle as claimed in claim 55 comprising a visual indiciapattern wherein each cluster of six triangular elements on eachhexagonal face has a specific visual indicium common to each of the sixtriangular elements.
 57. The logical puzzle as claimed in claim 55wherein the visual indicia pattern further comprises visual indiciadisplayed on the pentagonal faces, thereby challenging a user of thepuzzle to attempt to position the reassembled cluster adjacent a side ofthe pentagonal face having the visual indicium corresponding to thevisual indicium displayed on the elements of the cluster.
 58. Thelogical puzzle as claimed in claim 55 wherein the visual indicia patterncomprises one of up to twenty different visual indicia S1 to S20 foreach cluster of six sliding elements associated with each of the twentyhexagonal faces of the puzzle, and further comprises twelve additionalvisual indicia S21 to S32 for identifying the pentagonal faces of theBuckyball polyhedron.